%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ANA013-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:51:06 AM UTC 2026
% Result : Unsatisfiable 0.08s 5.56s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 8 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_1,VAR_1,VAR_0)
| ~ class_Orderings_Oorder(VAR_0) ),
file('theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
cnf(c_1,plain,
( c_lessequals(B,B,A)
| ~ class_Orderings_Oorder(A) ),
inference(clausify,[status(thm)],[cls_Orderings_Oorder__class_Oaxioms__1_0]) ).
fof(cls_conjecture_0,axiom,
! [VAR_0] : ~ c_lessequals(c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_f(v_x(VAR_0)),t_b),t_b),c_times(VAR_0,c_HOL_Oabs(v_f(v_x(VAR_0)),t_b),t_b),t_b),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_2,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_f(v_x(A)),t_b),t_b),c_times(A,c_HOL_Oabs(v_f(v_x(A)),t_b),t_b),t_b),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(tfree_tcs,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('theBenchmark.p',tfree_tcs) ).
cnf(c_3,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(clausify,[status(thm)],[tfree_tcs]) ).
fof(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
! [VAR_0] :
( class_Orderings_Oorder(VAR_0)
| ~ class_Ring__and__Field_Oordered__idom(VAR_0) ),
file('theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
cnf(c_4,plain,
( class_Orderings_Oorder(A)
| ~ class_Ring__and__Field_Oordered__idom(A) ),
inference(clausify,[status(thm)],[clsrel_Ring__and__Field_Oordered__idom_44]) ).
cnf(c_5,plain,
~ class_Orderings_Oorder(t_b),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_6,plain,
class_Orderings_Oorder(t_b),
inference(resolve,[status(thm)],[c_3,c_4]) ).
cnf(c_7,plain,
$false,
inference(resolve,[status(thm)],[c_5,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA013-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.54 % Computer : n005.cluster.edu
% 0.08/5.54 % Model : x86_64 x86_64
% 0.08/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.54 % Memory : 8046.5625MB
% 0.08/5.54 % OS : Linux 6.8.0-71-generic
% 0.08/5.54 % CPULimit : 300
% 0.08/5.54 % WCLimit : 300
% 0.08/5.54 % DateTime : Sat Sep 26 22:04:07 UTC 2026
% 0.08/5.54 % CPUTime :
% 0.08/5.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.54 % Process 3202020 was started by sandbox on n005,
% 0.08/5.54 % Sat Sep 26 22:04:07 2026
% 0.08/5.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.54
% 0.08/5.54 % From the command line: assign(max_seconds, 300).
% 0.08/5.56
% 0.08/5.56 % SZS status Unsatisfiable for theBenchmark
% 0.08/5.56
% 0.08/5.56 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/5.56 % Length of proof is 7.
% 0.08/5.56 % Level of proof is 2.
% 0.08/5.56 % Maximum clause weight is 0.000.
% 0.08/5.56 % Given clauses 0.
% 0.08/5.56
% 0.08/5.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------